ZX-Calculus:Trace-Indexed Dependent Types and Epistemic Semantics
We propose ZX-Calculus (Knowledge Evolution Calculus), a conservative extension of Martin-Lof Dependent Type Theory (MLTT) integrating trace-indexed types, presheaf non-monotone semantics, and constructive AGM belief revision. A Coq mechanisation accompanies the paper (34 complete proofs; zero admits for the two central results). (I) Trace types. FinTrace(s0,sn) is an inductive family of typed execution traces. FinTrace and Star(Step) are isomorphic as path types but not judgementally equal; TraceElim exposes the event label e:Event explicitly, giving a more ergonomic interface for event-driven induction. We prove the Trace-Reachability Correspondence, Deterministic Replay, and a canonici...
| Authors | Peng Chen |
|---|---|
| Primary category | cs.LO |
| Published | 2 June 2026 |
| Last updated at source | 2 June 2026 |
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